I have found the nebenkern in its perfect condition (fig. 7) only in material fixed in Flemming; although Zenker’s fixation showed some of the breaking-up stages. This may be due partly to poorer fixation in other mixtures and partly to chance, as not so many testes fixed in other agents were examined, and the appearance evidently represents a very brief stage. These fibers now begin to break up, and we get figures that remind one of Meves’s “mitochondrion körper”; that is, a darker staining center and radiating lines to the outer ring. (Fig. 11.) Sometimes stages a little later recall Paulmier’s “blackberry stage.” (Figs. 12 and 25.) Fig. 19_a_ is a surface view and fig. 19_b_ an optical section of a nebenkern that is in the process of breaking up. Figs. 20 and 21 have a part of one end cut off, while fig. 23 is a polar view. Fig. 22 is probably a forming blackberry stage. All the above are brief stages, and we soon get the appearance of figs. 13-16. Here we have the darkly staining central ball surrounded by a clear space, enclosed by a ring, as Meves (’00) found it in _Pygæra_. The central ball sometimes shows vacuoles (fig. 16), but most frequently stains as one mass. In some cysts with cells resembling fig. 16, it is difficult to distinguish between nucleus and nebenkern, yet the latter’s stain is never as intense as that of chromatin. The stages shown in figs. 13 and 14 persist for a long time, and it is probable that this is the end of the telophase and the beginning of the spermatid transformations. I have treated the above more in detail and shown more drawings than its importance may deserve, but it is in these stages that _Gryllus_ seems to differ from other species, and I have tried to describe and illustrate the appearances and changes fully. As the cell elongates, the axial filament grows out, the nebenkern approaches it, and a junction is effected in such a way that the axial filament runs over the surface of the nebenkern. (Figs. 18, 27, 28, and 30.) At first the nebenkern is still almost round, but it begins to elongate and the dark inner ball sends out a protrusion to the nucleus, and sometimes back to the point of separation between the external envelope and the axial filament. The outside ring disappears and the dark mass moves down the axial filament. (Fig. 31.) In many cases it breaks up into several small drops, which appear at intervals on the axial filaments. (Figs. 34 and 36.) In fig. 38 is seen such a hanging drop. In this way the nebenkern material is distributed over the axial filament and forms a sheath around it. [A] Professor McClung, Mr. Sutton, and Mr. Blackman, of Kansas University, and Doctor Child and Mr. Harper, of Chicago University, have seen my preparations, and all confirm my statement that the appearance is _not_ an artefact. 2.—_The Acrosome._